Linear Algebra

The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector spaces.

for a given complex Hermitian matrix

the linear span (also called the linear hull or just span)

In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A

Sylvester did important work on matrix theory

The Steinitz exchange lemma is a theorem in linear algebra concerning bases, dimensionality of a vector space, stating that for an

In mathematics, specifically linear algebra, the Woodbury matrix identity - named after Max A.

In geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated with a ellipsoid or hyperboloid

In mathematics, and more specifically in linear algebra, a linear map, linear mapping, or linear operator is a particular kind of

In linear algebra, particularly projective geometry, a semilinear map between vector spaces V and W over a field K is a function t

e Schur complement is a key tool in the fields of linear algebra, the theory of matrices, numerical analysis, and statistics.

In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the f

In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita

In linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition.

In linear algebra and matroid theory, Rota's basis conjecture is an unproven conjecture concerning rearrangements of bases, named

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as

MMT) is a result in enumerative combinatorics and linear algebra.

Cholesky is primarily remembered for the development of a form of matrix decomposition known as the Cholesky decomposition

In 1750 he published Cramer's rule, giving a general formula for the solution for any unknown in a linear equation system having a unique solution, in terms of determinants implied by the system.

Linear systems are a fundamental part of linear algebra, a subject used in most modern mathematics.

It may be expressed in several ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators.

Algebra Linear Algebra

Algebra Linear Algebra

Algebra Linear Algebra

The Motzkin-Taussky theorem is a result from operator and matrix theory about the representation of a sum of two bounded

gives a necessary and sufficient condition for two complex matrices to be unitarily equivalent. It is named after

Élie Cartan and Jean Dieudonné, establishes that every orthogonal transformation in an n-dimensional symmetric bilinear space

In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have

result in the perturbation theory of the eigenvalue of a complex-valued diagonalizable matrix. In its substance, it states an absolute upper

Sinkhorn's theorem states that every square matrix with positive entries can be written in a certain

used in two distinct senses for two different properties: linearity of a function (or mapping); linearity of a polynomial. An example

Takakazu Seki was a Japanese mathematician who was the first person to study determinants. He also discovered Bernoulli numbers before Jacob Bernoulli.